Inspired by a book titled  Harmonograph: A Visual Guide to the Mathematics of Music , I decided to program an interactive 3d harmonograph using

Here's what it looks like:

But just what is a Harmonograph? (from Wikipedia):

"A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are Lissajous curves, or related drawings of greater complexity.(...) A simple, so-called 'lateral' harmonograph uses two pendulums to control the movement of a pen relative to a drawing surface. One pendulum moves the pen back and forth along one axis and the other pendulum moves the drawing surface back and forth along a perpendicular axis. By varying the frequency of the pendulums relative to one another (and phase) different patterns are created. Even a simple harmonograph as described can create ellipses, spirals, figure eights and other Lissajous figures."

I decided to share the source code under the GPL license. The project is still work in progress, so the code is shared as is. It should be easy enough for anyone interested in interacting with this software to download the source code and run it in the Processing IDE on any platform.

Using this software, many variables can be interacted with to change the harmony of the graph. The interface is simple and very straight forward. The menu and variable names should be self explanatory. Here's the basics on how to interact with this program:

Mouse: Changes the point of view around the drawing
Numbers(1to9) quick: Recalls a pattern (variable values set)
Numbers(1to9) held: Saves/overwrite a variable preset for that number
Space bar: Shows/hide the 3d menu, menu is best viewed when the camera is centered, bring the mouse to the middle of the screen
Up/Down: Change from a variable to the next/previous
Left/Right: Increment/Decrement the variable

Source on GitHub:


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